If \(m=1\)  and \(p\)  is odd, there are two orbits belonging to \([l,m,n]\) ;
other values of \(m\)  give a unique orbit (see [1]}). Hence,
using that \(|\operatorname{GL}_n({\mathbb {F}}_p)| = \prod _{i=0}^{n-1}(p^n-p^i)\) , and dividing
by the total number of quadratic forms of dimension \(n\) , we obtain the
values of \(\pi _0(l,m,n)\)  recorded in the next lemma. Note that the
only form in the class \([0,0,n]\)  is the form where all the
coefficients are zero.
